Exam 18: Statistical Applications in Quality Management

The C_pk is a one-sided specification limit.

Variation signalled by individual fluctuations or patterns in the data is called _______.

C_pk > 1 indicates that the process average is exactly three standard deviations away from the closest specification limit.

Instruction 18-2 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic. Day Number of Papers Deliverd on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 -Referring to Instruction 18-2,what is the numerical value of the centre line for the p chart?

Instruction 18-11 Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select eight students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows. Day Range Mean Std. Dev 1 10 5.250 3.4949 2 31 15.250 10.3060 3 13 20.375 4.9262 4 21 22.875 8.3911 5 35 8.500 11.3767 6 18 7.875 6.9372 7 25 11.250 8.5815 8 30 7.875 9.5235 9 17 10.250 6.3640 10 22 9.500 7.8740 11 27 7.875 8.7086 12 26 12.875 9.3723 -Referring to Instruction 18-11,the chart is to be used for the time required to register.One way to obtain the control limits is to take the grand mean and add and subtract the product of A₂ times the average of the sample ranges.For this data set,the value of A₂ is _______

Special or assignable causes of variation are signalled by individual fluctuations or patterns in the data.

Instruction 18-10 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below. She also decides that the upper specification limit is 10 blemishes. Day 1 2 3 4 5 Mean Range 1 8 10 14 6 5 8.6 9 2 8 13 6 6 10 8.6 7 3 10 12 7 7 9 9.0 5 4 5 9 12 7 10 8.6 7 5 8 3 8 9 10 7.6 7 6 9 7 9 6 9 8.0 3 7 10 10 5 7 6 7.6 5 8 10 9 10 6 5 8.0 5 9 6 10 6 9 9 8.0 4 10 6 9 8 6 8 7.4 3 11 8 5 6 10 10 7.8 5 12 6 4 7 7 12 7.2 8 13 7 5 7 6 9 6.8 4 14 5 8 8 7 6 6.8 3 15 7 12 10 6 10 9.0 6 16 7 11 4 7 8 7.4 7 17 8 4 5 4 7 5.6 4 18 11 4 11 11 10 9.4 7 19 6 10 6 10 10 8.4 4 20 6 12 12 6 8 8.8 6 -Referring to Instruction 18-10,an R chart is to be constructed for the number of blemishes.The centre line of this R chart is located at _______.

Instruction 18-5 The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follow. Day Number Poor Proportion Poor 1 33 0.0550000 2 29 0.0483333 3 31 0.0516667 4 32 0.0533333 5 43 0.0716667 6 45 0.0750000 7 46 0.0766667 8 48 0.0800000 9 48 0.0800000 10 46 0.0766667 11 28 0.0466667 12 32 0.0533333 13 28 0.0466667 14 32 0.0533333 15 31 0.0516667 16 24 0.0400000 -Referring to Instruction 18-5,a p control chart is to be constructed for these data.The lower control limit is _______,while the upper control limit is _______.

Instruction 18-1 Below is the number of defective items from a production line over 20 consecutive morning shifts. Day Nonconf. Day Nonconf. 1 26 11 22 2 27 12 26 3 23 13 21 4 21 14 22 5 26 15 19 6 20 16 17 7 35 17 21 8 30 18 18 9 21 19 16 10 25 20 17 Note: Nonconf. = Nonconformances -Referring to Instruction 18-1,based on the c chart,there appears to be a special cause of variation in the process.

The control limits are based on the standard deviation of the process.

Instruction 18-12 The manufacturer of canned food constructed control charts and analysed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 kg. The table below provides the range and mean of the weights of five cans tested every 15 minutes during a day's production. Number XBar Range Number XBar Range 1 3.05072 0.0215 16 3.04646 0.073 2 3.01228 0.087 17 3.03868 0.0696 3 3.03558 0.0851 18 3.03338 0.0329 4 3.01014 0.0674 19 3.03322 0.0455 5 3.00858 0.0983 20 3.05078 0.0215 6 3.02704 0.0527 21 3.04808 0.0396 7 3.04268 0.0508 22 3.05348 0.0581 8 3.01052 0.0791 23 3.05516 0.0682 9 3.03464 0.0663 24 3.03426 0.0325 10 3.02034 0.0538 25 3.0516 0.0641 11 3.03764 0.0584 26 3.05562 0.0809 12 3.0409 0.0434 27 3.04402 0.0374 13 3.0519 0.0762 28 3.06458 0.0284 14 3.03994 0.0833 29 3.0544 0.0738 15 3.03788 0.0601 -Referring to Instruction 18-12,an R chart is to be constructed for the weight.The center line of this R chart is located at _______

Instruction 18-10 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below. She also decides that the upper specification limit is 10 blemishes. Day 1 2 3 4 5 Mean Range 1 8 10 14 6 5 8.6 9 2 8 13 6 6 10 8.6 7 3 10 12 7 7 9 9.0 5 4 5 9 12 7 10 8.6 7 5 8 3 8 9 10 7.6 7 6 9 7 9 6 9 8.0 3 7 10 10 5 7 6 7.6 5 8 10 9 10 6 5 8.0 5 9 6 10 6 9 9 8.0 4 10 6 9 8 6 8 7.4 3 11 8 5 6 10 10 7.8 5 12 6 4 7 7 12 7.2 8 13 7 5 7 6 9 6.8 4 14 5 8 8 7 6 6.8 3 15 7 12 10 6 10 9.0 6 16 7 11 4 7 8 7.4 7 17 8 4 5 4 7 5.6 4 18 11 4 11 11 10 9.4 7 19 6 10 6 10 10 8.4 4 20 6 12 12 6 8 8.8 6 -Referring to Instruction 18-10,an R chart is to be constructed for the number of blemishes.The upper control limit for this data set is _______.

Instruction 18-2 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic. Day Number of Papers Deliverd on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 -Referring to Instruction 18-2,what is the numerical value of the lower control limit for the p chart?

In Australia,control limits on a control chart are placed so that they are three standard deviations above and below a central line.

Instruction 18-10 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below. She also decides that the upper specification limit is 10 blemishes. Day 1 2 3 4 5 Mean Range 1 8 10 14 6 5 8.6 9 2 8 13 6 6 10 8.6 7 3 10 12 7 7 9 9.0 5 4 5 9 12 7 10 8.6 7 5 8 3 8 9 10 7.6 7 6 9 7 9 6 9 8.0 3 7 10 10 5 7 6 7.6 5 8 10 9 10 6 5 8.0 5 9 6 10 6 9 9 8.0 4 10 6 9 8 6 8 7.4 3 11 8 5 6 10 10 7.8 5 12 6 4 7 7 12 7.2 8 13 7 5 7 6 9 6.8 4 14 5 8 8 7 6 6.8 3 15 7 12 10 6 10 9.0 6 16 7 11 4 7 8 7.4 7 17 8 4 5 4 7 5.6 4 18 11 4 11 11 10 9.4 7 19 6 10 6 10 10 8.4 4 20 6 12 12 6 8 8.8 6 -Referring to Instruction 18-10,an R chart is to be constructed for the number of blemishes.One way to create the upper control limit involves multiplying the mean of the sample ranges by D_4. For this data set,the value of _D4 is _______.

Instruction 18-1 Below is the number of defective items from a production line over 20 consecutive morning shifts. Day Nonconf. Day Nonconf. 1 26 11 22 2 27 12 26 3 23 13 21 4 21 14 22 5 26 15 19 6 20 16 17 7 35 17 21 8 30 18 18 9 21 19 16 10 25 20 17 Note: Nonconf. = Nonconformances -Referring to Instruction 18-1,based on the c chart,it appears that the process is out of control.

Instruction 18-4 A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows. Day Bad \% Bad 1 9 0.037500 2 7 0.029167 3 4 0.016667 4 6 0.025000 5 8 0.033333 6 3 0.012500 7 6 0.025000 8 10 0.041667 9 16 0.066667 10 24 0.100000 11 15 0.062500 12 9 0.037500 13 4 0.016667 14 8 0.033333 15 6 0.025000 -Referring to Instruction 18-4,construct a p control chart for these data.

Which of the following is NOT one of Deming's 14 points?

Which famous statistician developed the 14 points of management?

Instruction 18-2 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic. Day Number of Papers Deliverd on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 -Referring to Instruction 18-2,what is the numerical value of the upper control limit for the p chart?